Positive displacement (PD) type gas-transfer machinery can be grouped into two categories, compressors and expanders, as shown in FIG. 1a. PD type compressors convert shaft energy into gas internal energy by trapping a fixed amount of gas into a cavity, then transferring, compressing and discharging it into the outlet pipe. On the other hand, PD type expanders convert gas internal energy back to shaft energy by an opposite cycle of the compressor. In a broad sense, the gas media includes different gases or liquid vapor or mixture of gases and/or liquid. The following description will be focused on compressor for gas, but the problems involved and the principle and methods of improvement are the same for expander and for other types of gas media in general. As used herein, the term “gas” is intended to be broadly construed to mean “fluid”, and as such means “gas, liquid, or gas/liquid mixtures.”
Compared with dynamic type compressors, PD compressors are capable of generating a wide range of pressures and flows and are suited for various applications because of the many different types that have been developed over the years. For example, positive displacement compressors can be further classified according to the mechanism used to move the gas, including rotary type (such as Roots (lobe), screw, and scroll) and reciprocating type (such as piston and diaphragm), as further shown in FIG. 1a. Though each type of PD compressor has its own unique shape, movement, operating principle and pros and cons, they all have in common a flow suction port, a volume-trapping cavity (aka gas transfer chamber) and a flow discharge port where a valve controls the timing of the release of gas media. Moreover, they are all cyclic in nature and possess the same compression cycle for the transferred gas, that is, suction, trap, compression, discharge and dampening.
FIG. 2a shows two flow charts of a compression cycle (top figure is under-compression, bottom figure is over-compression) for a generic conventional positive displacement compressor and FIGS. 2b-2e show examples of the compression cycle and structure for the common PD types of Roots, screw, scroll and reciprocating, respectively. Gas flows from the suction port into the compressor cavity where the gas media gets trapped after closing of the compressor inlet port and is then transferred and compressed (where the trapped cavity volume is reduced). After a desired volume reduction ratio (or so-called internal compression ratio) is reached, the discharge valve at the flow discharge port is opened and gas flows out into the compressor outlet.
According to conventional theory, there are two distinct thermodynamic processes that occur most often for a PD compressor or expander. The thermodynamic process is adiabatic when compressor or expander discharge pressure is equal to system back pressure (or 100% internal compression or expansion). At this ideal design condition, compressor or expander efficiency, pulsation and induced vibration and noise are most desirable. But more often, a PD compressor or expander operates at off-design conditions where the discharge pressure is either lower or higher than the system back pressure caused by the inherent nature of possessing a fixed built-in volume ratio. The resulting processes are often called under-compression (UC) (also referred to as over-expansion, or OE) and over-compression (OC) (or under-expansion, UE), and the thermodynamic process suddenly changes to iso-choric (constant volume), as shown in the left (UC) and right (OC) figures of FIG. 1b. The compressor or expander efficiency, pulsation and induced vibration and noise become worse at these off-design conditions and some type of controls are always desired such as a variable geometry and/or a discharge dampener (silencer) in order to minimize deviation from the ideal design condition. According to the conventional theory, a UC or OC process would result in a rapid induced fluid flow (IFF) into or out of the compressor cavity, as shown in FIG. 2a, that takes place one pulse per cavity passing at discharge, the primary driving force of gas pulsations. Since all PD compressors divide the incoming gas stream mechanically into parcels of cavity size for delivery to the discharge, they inherently generate pulsations with cavity passing frequency whenever operating under off-design conditions of either an under-compression or over-compression. An extreme under-compression case is the Roots type blower, shown in FIG. 2b, which has no internal compression or the pulsation magnitude is directly proportional to pressure rise from the compressor inlet to outlet and the resulting compression process is purely iso-choric, according to the conventional theory.
The gas pulsation amplitudes are especially significant under elevated pressure conditions, such as in air conditioning and refrigeration or for operating far away from the design condition. Quantitatively, there are orders of magnitude difference between acoustic waves and gas pulsations, though both are pressure fluctuations. For example, acoustic waves are often limited to pressure fluctuations below 140 dB, equivalent to a pressure level of 0.002 Bar or 0.03 psi. For industrial PD type gas machinery, the measured gas pulsations are typically in the ranges of 0.02-2 Bar or 0.3-30 psi (can be even higher), or equivalent to 160-200 dB. So gas pulsation pressure levels are much higher and well beyond the pressure range modeled for the linear acoustics. Moreover, the gas pulsations generated by the compressor discharge pressure difference generally stay within the gas line (often called gas borne) and are periodic in nature. These unsteady gas-pulsation forces would travel at the speed of the wave throughout the downstream piping system and if left uncontrolled, could potentially damage or fatigue pipe lines and equipment, and excite severe vibrations and noises.
To control gas pulsations, a large conventional dampener, usually consisting of several sudden area change plenums connected through a number of chokes (e.g., perforated tubes), is typically located at the flow discharge and connected in series with the discharge port of the transfer chamber of the positive displacement compressors, as shown in FIGS. 2a-2e. This conventional serial dampener is very effective in gas pulsation attenuation, typically in the range of 20-40 dB, as shown by the experimental results plotted in FIG. 4g, but it is often heavy and bulky in size, which creates secondary problems like inducing more vibration and noises due to additional surface area and sheet metal construction, which potentially could result in dampener structure fatigue failures and catastrophic damages to downstream components and equipments.
Moreover, conventional serial dampeners used widely today create additional back pressure that the compressor has to overcome, resulting in doing more work as shown in FIG. 4f, hence reducing overall system efficiency across the whole flow range. In addition, compressor efficiency suffers even more at off-design conditions, especially in an over-compression condition. The traditional solution is to use a variable geometry design so that the internal compression ratio can be adjusted to meet different operating conditions. This solution is very complicated structurally with high cost and low reliability. For this reason, PD compressors are often cited unfavorably due to high gas pulsations and induced vibration, noise, and harshness (NVH), and low compressor efficiency, when compared with dynamic type compressors like centrifugal or axial compressors. At the same time, the ever-stringent environmental regulations from the government and growing public awareness of the comfort level in residential and office applications have given rise to an urgent need for quieter and more efficient PD compressors.
Various attempts have been made to replace the conventional serially connected discharge dampener or silencer. One example replacement device for Roots type PD compressors, as disclosed in U.S. Pat. No. 4,215,977 to Weatherston, is designed to feed back a portion of the outlet flow through an injection port to the compressor cavity prior to discharge, in an attempt to equalize the cavity pressure with the outlet hence reducing the pressure spike when the cavity is suddenly exposed to the higher outlet pressure. Other example replacement devices include those for screw compressors as disclosed in U.S. Pat. No. 5,051,077 to Yanagisawa and those for scroll compressors as disclosed in U.S. Pat. No. 5,370,512 to Fujitani et al. However, their effectiveness for gas pulsation attenuation is very limited (e.g., to the level of 5-8 dB, a 2-fold attenuation, as shown by experimental results in FIG. 4g), and as such a discharge dampener is still needed in most applications.
It is well known that technological advance is often triggered by new knowledge of the same phenomenon. A new understanding of the gas pulsation and under-compression phenomena will now be discussed. It relates to an unconventional shock tube hypothesis for gas pulsations and under-compression mechanisms. To help understand the theoretical roots, see generally, Huang, P. X., Gas Pulsations: A Shock Tube Mechanism. The 2012 International Compressor Engineering Conference at Perdue, 2012, and Under Compression: An Isochoric or Adiabatic Process? The 2012 International Compressor Engineering Conference at Perdue, 2012. The shock tube mechanism is based on the well studied physical phenomenon as it occurs in a classical shock tube where a diaphragm separates a region of high-pressure gas from a region of low-pressure gas inside a closed tube, as shown in FIGS. 3a-3b. According to the shock tube theory, when the diaphragm is suddenly broken, a series of expansion waves is generated, propagating from low-pressure to high-pressure regions at the speed of sound, and simultaneously a series of compression waves quickly coalesces (fully developed) into a shockwave, propagating from high-pressure to low-pressure regions at a speed faster than the speed of sound, inducing rapid fluid flow behind the wave front at the same time.
By analogy, the sudden opening of the diaphragm separating the high and low pressure gases in a shock tube is just like (analogous to) the sudden opening of the compression cavity to the flow discharge port under off-design conditions, because both are transient in nature and driven by the same forces from a suddenly exposed pressure difference. By this correlation, the well established results of the shock tube theory can be readily used to offer insights into mechanism for both gas pulsation and under-compression of any PD type gas machinery such as compressor or expander.
This shock tube mechanism can be summarized into the following gas pulsation rules for industrial gas pulsations that far exceed the upper limit of 140 dB of the classical acoustics. The gas pulsation rules are intended as a simplified way to answer some of the fundamental questions of gas pulsations and under-compression such as: What is the physical nature of gas pulsation and under-compression phenomena? What exactly triggers their happening and where/when? How to estimate quantitatively their magnitude? In principle, these rules are applicable to different gases and for any PD type gas machinery or devices such as engines, expanders, pressure compressors, and vacuum pumps.                1. Rule I: For any two divided compartments, either moving or stationery, with different gas pressures p1 and p4, there will be no or little gas pulsations generated if the two compartments stay divided (or isolated from each other).        2. Rule II: If, at an instant, the divider between the high pressure gas p4 and the low pressure gas p1 is suddenly removed, gas pulsations are instantaneously generated at the location of the divider and at the instant of the removal as a composition of a fan of compression waves (CW) (or a quasi-shockwave), a fan of expansion waves (EW) and an induced fluid flow (IFF), with magnitudes as follows:CW=p2−p1=p1[(p4/p1)1/2−1]=(p4×p1)1/2−p1  (1)EW=p4−p2=CW*(p4/p1)1/2=p4−(p4×p1)1/2  (2)ΔU=(p2−p1)/(ρ1×W)=CW/(ρ1×W)  (3)         where ρ1 is the gas density at low pressure region, W is the speed of the lead compression wave, and ΔU is the velocity of Induced Fluid Flow (IFF).        3. Rule III: Pulsation component CW is the action by the high pressure (p4) gas to the low pressure (p1) gas, while pulsation component EW is the reaction by low pressure (p1) gas to high pressure (p4) gas in the opposite direction, and their magnitudes are such that they approximately divide the pre-opening pressure ratio p4/p1, that is, p2/p1=p4/p2=(p4/p1)1/2. At the same time, CW and EW pair together to induce the third pulsation component, a unidirectional fluid flow IFF in a fixed formation of CW-IFF-EW.        
In general, these gas pulsation rules explain the relationship between an under-compression (or over-compression) and gas pulsations as a cause (pre-opening pressure difference p4−p1) and the effect (post-opening results) that are the two aspects of the same phenomena. Moreover, Rules I & II give the two sufficient conditions that link the under-compression and gas pulsation events, which are:                a) the existence of a pressure difference p4−p1 from either an under-compression or over-compression; and        b) the sudden opening of the divider separating the pressure difference p4−p1.Based on these two conditions, it can be determined that the location and moment that trigger the under-compression action and gas pulsation generation are at the discharge and at the instant when the discharge port suddenly opens. Because all PD compressors or expanders convert energy between the shaft and the gas by dividing the incoming continuous gas stream into parcels of cavity size and then discharging each cavity separately at the end of each cycle, there always exists a “sudden” opening at the discharge phase to return the discrete gas parcels back to a continuous gas stream again. Therefore both sufficient conditions are satisfied at the moment of the discharge opening if the compressor or expander operates at off-design conditions such as an UC (OE) or OC (UE).        
Rule I also implies that there would be no or little gas pulsations during the suction, trap/transfer and internal compression (expansion) phases of a cycle because of the absence of either a pressure difference (p4−p1) or a sudden opening. The focus instead should be placed upon the discharge phase, especially at the moment when the discharge port is suddenly opened and under off-design conditions like either an UC (OE) or OC (UE).
Rule II also reveals the nature and composition of gas pulsations as a combination of large amplitude compression waves (CW) (or a quasi-shockwave), a fan of expansion waves (EW) and an induced fluid flow (IFF). These waves are non-linear waves with ever-changing wave-fronts during propagation. This is in direct contrast to the acoustic waves that are linear in nature and whose wave-fronts stay the same and do not induce a mean through-flow. It is also noted that the three different components (CW, EW and IFF) are generated as a homologous, inseparable whole simultaneously and in a fixed formation CW-IFF-EW. It is believed that this formation reflects the dynamics of the transient under-compression and pulsation events with the wave-fronts CW and EW as the moving forces driving the IFF in between. In turn, the source of CW and EW is simply a re-distribution of the pre-opening under-compression pressure difference Δp41 that is now being suddenly released and turned into a moving force pushing the flow (IFF) at the front (CW) and pulling the flow (IFF) from behind (EW) at the same time. This new physical picture implies that gas pulsations would be difficult to control because it's not one component (not just IFF as suggested by the conventional theory) but all three components have to be dealt with as a whole.
Rule III shows further that the interactions between two gases at different pressures are mutual so that for every CW pulsation, there is always an equal but opposite EW pulsation in terms of pressure ratio (p2/p1=P4/p2). Teamed together, they induce a unidirectional fluid flow pulsation (IFF) in the same direction as the compression waves (CW).
To better understand the gas pulsation mechanism in light of the gas pulsation rules, let's review the Roots example illustrated in FIG. 3c (left figure) again and why just a pre-opening is not enough even though it elongates the time for the gas to discharge. From FIG. 3c (right figure), it can be seen that the prior art failed to recognize that the cavity opening would generate a series of compression waves (CW) into the compressor cavity and simultaneous expansion waves (EW) in the opposite direction down-stream. The EW waves have a magnitude of pressure difference Δp42 even greater than the pressure difference Δp21 of CW and are left loose to travel downstream at the speed of sound. This mechanism suggests that any effective control has to deal with the combined EW and IFF effects together as the dominant source of gas-borne pulsations for positive displacement gas machinery.
To better understand the UC mechanism in light of the gas pulsation rules, let's examine the above example again. According to the conventional theory, when the cavity gas is suddenly opened to the higher pressure gas at outlet as shown in FIG. 3c (left figure), a backflow would rush in compressing the gas inside the cavity iso-chorically. However, according to the shock tube theory, the cavity opening phase in FIG. 3c (left figure) resembling the diaphragm bursting of a shock tube would generate a series of compression waves (CW) into the cavity as shown in FIG. 3c (right figure). The wave-front sweeps through the low pressure gas and compresses it at the same time at the speed of wave. This results in an almost instantaneous wave compression well before the backflow (behind the contact surface) could arrive because the CW wave travels much faster than the fluid flow (IFF). In this view, the CW waves are the primary force for the under-compression while the back-flow is simply an induced gas flow behind the wave after compression takes place. According to the shock tube theory, the wave compression process is adiabatic thermodynamically and governed by the Rankine-Hugoniot Equation, not the Amonton Law for an isochoric process.
Accordingly, it can be seen that needs exist for improvements in positive displacement machinery for reducing gas pulsations to provide induced NVH reductions and improved machinery efficiencies.